Annu. Rev. Astron. Astrophys. 1994. 32: 531-590 Copyright © 1994 by Annual Reviews. All rights reserved

7.4. The Effect of Microlensing on Quasar Density

Quasars that are not bright enough to be included in a flux-limited sample may be amplified by quasar microlensing, thereby bringing them above the detection threshold (Turner 1980, Canizares 1981, Peacock 1982, Schneider et al 1992) and modifying the apparent number density. This effect depends strongly on the quasar luminosity function, which may itself be influenced by lensing (Vietri & Ostriker 1983). There are several indications that this happens. For example, Webster et al (1988) found that faint galaxies were 4.4 times as numerous as usual within 6 arcsec of high redshift quasars and attributed this to the galaxies enhancing the quasar density. However, to explain such a high enhancement, they had to attribute to the galaxies unrealistically massive halos (Hogan et al 1989), so the origin of this effect is not well understood.

A similar result was found by Hammer & Le Fevre (1990), who found the quasar density within 5 arcsec of z > 1 radio galaxies to be nine times greater than expected; Bartleman & Schneider (1993) claim that this can be explained if the quasar luminosity function is sufficiently steep. Rix & Hogan (1988) have claimed a lower limit of _C(0.001-10¹⁰ M) > 0.25 from an excess of quasar-galaxy pairs in the Einstein Medium Source Survey, but Dalcanton et al (1994) argue that they underestimate the amplification (and hence overestimate _C) by underestimating the steepness of the quasar luminosity function. Kovner (1991) obtains constraints on _C(0.001-10¹⁰ M) by studying the slope of the bright quasar counts.

Rodrigues-Williams & Hogan (1994) have found an excess of quasars in the direction of clusters. Their sample comprises 129 quasars with 1.4 < z < 2.2 and 70 clusters at z ~ 0.2; they find an overdensity of 1.7. Unfortunately, this does not seem to be consistent with the most plausible mass distribution. Note that there is also a lensing effect that reduces the number of quasars near clusters because the background area is expanded. Which effect wins depends on the steepness of the quasar luminosity function. The amplification effect wins when the luminosity function is steep, but the spread effect wins when it is shallow. There may also be evidence for the second effect: Boyle et al (1988) have found a 30% deficit of high redshift quasars within 4 arcsec of clusters, although they attribute this to the effect of dust.